### Table 3: Quartic

1991

Cited by 7

### Table 4: Quartic elds

### Table 7. Summary of multiplicative costs for quartic extensions as direct quartic

"... In PAGE 12: ... Then the total cost for Toom-Cook-4x multipli- cation is 7M +23MZ +76A+3B, and the total cost for Toom-Cook-4x squaring is 7S + 23MZ + 54A + 3B. Table7 shows the multiplicative costs for direct quartic extensions, and Ta- ble 8 shows the squaring costs for direct quartic extensions. Table 7.... ..."

### Table 8. Summary of squaring costs for quartic extensions as direct quartic

### Table 16. Quartic Correlation Sets

### Table 3 shows the relative computational time for the evalution of the bivariate kernels in relation to the Uniform kernel. In the Zortech-compiler, as in many other compilers, is an integrated optimizer. In the right column we see the relative computing time when using the optimizer. So we see that, for example, the Epanechnikov kernel needs 16% more time to evaluate the kernel values on the same data as the Uniform kernel (the data were uniformly distributed in the right upper quarter of the unit circle, see e.g. program A.1 for the Quartic kernel). If we do not use the optimizer the Uniform kernel takes more than 3 times longer to calculate the kernel values. Kernel

"... In PAGE 9: ... Table3 : Relative computational time of bivariate kernels We can distinguish two classes of kernels independent of using unoptimized code (286- code, large memory model, no optimization) or optimized code (386-code, extender, fully time-optimized, using the coprocessor). On the one side we have the polynomial ker- nels (Uniform, Quartic, Epanechnikov, Triangle and Triweight), on the other side the transcendental kernels (Cosine, Logarithm-1, Logarithm-2).... ..."

### Table 1: Quartic polynomial classi cation

"... In PAGE 4: ... Clearly, we have that m1 + m2 + + mr is just the degree of p. For example, all quartics belong to one of the categories of Table1 , which are in 1-1 correspondence with the partitions of four.... ..."

### Table 18: Joins of a quadratic and quartic

"... In PAGE 8: ... Two of the 26 integer relations entail join elds noted in [7], namely the rst in Table 16 and the second in Table 17. We used Pari apos;s nfisincl command to con rm that all 6 of the quartic invariant trace elds in Table18 are sub elds of the octadic joins. In 4 of these 6 cases, distinct values of b1=b2 occur, for the same invariant trace eld.... In PAGE 19: ... The 6 distinct values of (1) are Z3 = 1 vol(41) (50) Z23;3 = 1 3 vol(52) = 1 10 vol(949) (51) Z44;3 = 1 3 vol(948) (52) Z59;3 = 1 vol(74) (53) Z76;3 = 1 vol(935) (54) Z448;4 = 1 6 vol(818) (55) where the subscripts of ZjDj;n identify the (negated) discriminant and degree of the number eld, and we omit the latter in the quadratic case. Two further knots, 821 and 928, have invariant trace elds in Table18 . From these sub elds of joins, one may extract Z7 = 4 vol(821) ? 4 3 vol(818) (56) Z507;4 = 2 5 vol(928) ? 1 vol(41) (57) We now report on two very special knots at 10 crossings.... ..."

### Table 4: Symbolic regression with quartic polynomial as target

1999

Cited by 28

### Table 4: Symbolic regression with quartic polynomial as target

1999

Cited by 28